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Table 7 The values of \((q^*_S, q^*_C, q^*_D)\) that maximize the weighted sum throughput \(T_w\) for different values of \(M_U\) when \(\alpha = 0.7\) and the queue at S is unstable

From: A wireless caching helper system with heterogeneous traffic and random availability

\(\delta = 0.5\)
\(M_U\)   \(w = 1/4\) \(w = 2/4\) \(w = 3/4\)
200 max. \(T'_w\) 0.430 0.286 0.399
\((q^*_S, q^*_C, q^*_D)\) (0, 1, 0) (0, 1, 0) (1, 0.024, 1)
400 max. \(T'_w\) 0.398 0.289 0.404
\((q^*_S, q^*_C, q^*_D)\) (0, 1, 0) (1, 0.029, 1) (1, 0.005, 1)
600 max. \(T'_w\) 0.374 0.295 0.410
\((q^*_S, q^*_C, q^*_D)\) (0, 1, 0) (1, 0, 1) (1, 0.011, 1)
800 max. \(T'_w\) 0.354 0.295 0.416
\((q^*_S, q^*_C, q^*_D)\) (0, 1, 0) (1, 0, 1) (1, 0, 1)
1000 max. \(T'_w\) 0.337 0.298 0.422
\((q^*_S, q^*_C, q^*_D)\) (0, 1, 0) (1, 0, 1) (1, 0, 1)
\(\delta = 1.2\)
200 max. \(T'_w\) 0.189 0.363 0.537
\((q^*_S, q^*_C, q^*_D)\) (1, 0, 1) (1, 0, 1) (1, 0, 1)
400 max. \(T'_w\) 0.190 0.368 0.546
\((q^*_S, q^*_C, q^*_D)\) (1, 0.046, 1) (1, 0, 1) (1, 0.484, 1)
600 max. \(T'_w\) 0.190 0.371 0.552
\((q^*_S, q^*_C, q^*_D)\) (1, 0, 1) (1, 0, 1) (1, 0, 1)
800 max. \(T'_w\) 0.191 0.373 0.556
\((q^*_S, q^*_C, q^*_D)\) (1, 0, 1) (1, 0, 1) (1, 0, 1)
1000 max. \(T'_w\) 0.191 0.375 0.559
\((q^*_S, q^*_C, q^*_D)\) (1, 0, 1) (1, 0, 1) (1, 0, 1)